The dietary restriction against eating pork is part of the Law of Moses which is part of the Hebrew Bible, known to Christians as the Old Testament. The New Testament, however, contains passages which state that Christians are free from following the Law, including its dietary restrictions:

Romans 7:1-6 Do you not know, brothers and sisters - for I [Paul] am speaking to those who know the law - that the law has authority over someone only as long as that person lives? [...] So, my brothers and sisters, you also died to the law through the body of Christ, that you might belong to another, to him who was raised from the dead, in order that we might bear fruit for God. For when we were in the realm of the flesh, the sinful passions aroused by the law were at work in us, so that we bore fruit for death. But now, by dying to what once bound us, we have been released from the law so that we serve in the new way of the Spirit, and not in the old way of the written code.

Mark 7:18-23 He [Jesus] said to them, "Are you so without understanding also? Do you not know that anything from the outside that enters a man cannot defile him, because it does not enter his heart, but into his stomach, and goes out into the sewer, thus purifying all foods?" And He said, "What comes out of a man is what defiles a man. For from within, out of the heart of men, proceed evil thoughts, adultery, fornication, murder, theft, covetousness, wickedness, deceit, licentiousness, an evil eye, blasphemy, pride and foolishness. All these evil things come from within and defile a man."

Acts 10:12-16 In the sheet were all sorts of animals, reptiles, and birds. Then a voice said to him, "Get up, Peter; kill and eat them." "No, Lord," Peter declared. "I have never eaten anything that our Jewish laws have declared impure and unclean." But the voice spoke again: "Do not call something unclean if God has made it clean." The same vision was repeated three times. Then the sheet was suddenly pulled up to heaven.

Galatians 3:1-25 You foolish Galatians! Who has bewitched you? Before your very eyes Jesus Christ was clearly portrayed as crucified. I would like to learn just one thing from you: Did you receive the Spirit by the works of the law, or by believing what you heard? [...] Does God give you his Spirit and work miracles among you by the works of the law, or by your believing what you heard? [...]

For all who rely on the works of the law are under a curse, as it is written: "Cursed is everyone who does not continue to do everything written in the Book of the Law." Clearly no one who relies on the law is justified before God, because "the righteous will live by faith". The law is not based on faith; on the contrary, it says, "The person who does these things will live by them. Christ redeemed us from the curse of the law by becoming a curse for us, for it is written: "Cursed is everyone who is hung on a pole." He redeemed us in order that the blessing given to Abraham might come to the Gentiles through Christ Jesus, so that by faith we might receive the promise of the Spirit.

[...] Before the coming of this faith, we were held in custody under the law, locked up until the faith that was to come would be revealed. So the law was our guardian until Christ came that we might be justified by faith. Now that this faith has come, we are no longer under a guardian.

As these passages demonstrate, medieval Christians would have seen no contradiction in eating pork and adhering to the Bible. Dietary restrictions and others you've mentioned such as wearing clothes of mixed fabrics were considered to be part of the Jewish inheritance which no longer applied to believers who had been saved through Christ. In the Sermon on the Mount, Jesus says, "Don't think that I come to destroy the law or the prophets. I didn't come to destroy, but to fulfill." Christians have long argued over exactly what this means theologically, but by and large these New Testament passages have been interpreted by Christians throughout history as meaning that they are no longer bound by most aspects of the Mosaic Law (with notable exceptions like the Ten Commandments).

Medieval Christians did observe fasting, but it was not based on the dietary restrictions of the Old Testament. Instead, they were based on Jesus's forty days and forty nights of fasting in the desert when the Devil was trying to tempt him. The details of Jesus's fast are not given in the Biblical text, which merely says, "He fasted for forty days and forty nights and afterwards was hungry". This forty-day fast was replicated in the medieval liturgical calendar through the periods of Lent and Advent, which are the weeks leading up to Easter and Christmas respectively. Different liturgical councils in Late Antiquity and the Middle Ages gave various recommendations for how exactly people should fast during these periods. Monastic orders usually followed stricter fasts, but again, these were not dictated by the Law of Moses, but by a sense of restricting one's food and activities to avoid temptation and express penitence. Certain days of the week were also designated fast days, most famously Friday since Jesus died on a Friday.

The foods that people were expected to drop during fasts were based on creating an ascetic experience of deprivation, rather than on Old Testament dietary rules. Meat was the most commonly dropped food. It was a luxury, it was considered tasty, and according to some medieval theologians, consuming too much of it incited lust (thanks Thomas Aquinas). Medieval theologians did follow the old Jewish dietary restrictions in the sense of believing that the flesh of fish was of a different kind to the flesh of land-dwelling animals and birds, which is why fish became considered an acceptable form of sustenance during fasting. The logic went that Christ was a warm-blooded man who sacrificed himself, so on days commemorating that sacrifice, consuming the flesh of warm-blooded animals should be avoided. Eating fish on fasting days became a pro-Catholic political statement in post-Reformation England since Henry VIII made a point of flouting Catholic fasting laws by eating meat on Fridays, which may also be part of why that association is so strong today.

In conclusion, yes, following the Bible was incredibly important for early medieval Christians. But the New Testament, according to the most common interpretations at the time, exempted them from following Jewish dietary restrictions.